Suppose you are given a circle. Give a construction to find its centre.
Answers
★ Steps of construction :-
(a) Take any three points A, B and C on the circle.
(b) Join AB and BC.
(c) Draw perpendicular say LM of AB.
(d) Draw perpendicular PQ of BC.
(e) Let LM and PQ intersect at point O.
Then O is the centre of the circle.
★ Verification :-
O lies on the perpendicular of AB.
OA = OB ……….(i)
O lies on the perpendicular of BC.
OB = OC ……….(ii)
From eq. (i) and (ii), we observe that
OA = OB = OC = (say)
Three non-collinear points A, B and C are at equal distance (r) from the point O inside the circle.
Hence, O is the centre of the circle.
Answer:
Question ⤵
Suppose you have given a circle. Draw a construction .
Answer ⬇
★ Steps of construction :-
(a) Take any three points A, B and C on the circle.
(b) Join AB and BC.
(c) Draw perpendicular say LM of AB.
(d) Draw perpendicular PQ of BC.
(e) Let LM and PQ intersect at point O.
Then O is the centre of the circle.
★ Verification :-
O lies on the perpendicular of AB.
OA = OB ……….(i)
O lies on the perpendicular of BC.
OB = OC ……….(ii)
From eq. (i) and (ii), we observe that
OA = OB = OC = (say)
Three non-collinear points A, B and C are at equal distance (r) from the point O inside the circle.
Hence, O is the centre of the circle.
Thanks..
